Neuromorphic systems are of great interest for modeling and solving complex problems, offering an alternative to conventional deterministic computers1. They generally aim to emulate the functionality and structure of the human brain and thus require many independent true random noise signal sources. In recent years, the stochasticity of spin-transfer-torque switching of magnetic tunnel junctions (MTJs) has gained interest for such applications. Focusing on in-plane MTJs with low energy barriers, the devices investigated thus far have fast thermally driven random fluctuations2,3. However, they are highly susceptible to small changes in temperature and device parameters. Here we show the room-temperature operation of medium energy barrier (Δ=394) perpendicularly magnetized MTJs (pMTJs) in the ballistic switching limit (ns duration pulses) and discuss why their operation is much less sensitive to temperature and material parameters. In the ballistic limit the resulting junction state is random mainly because of the thermal distribution of the initial magnetization state. We denote this a stochastic magnetic actuated random transducer (SMART) device because the pulse activates the junction to generate a random bit stream, much like a coin flip. In fact, we analyze the stochastic nature of our SMART devices by comparing their statistics to that expected of Bernoulli trials (see Figs.1 and 2). We also test our bit stream with the NIST statistical test suite for random number generators which investigates their suitability for cryptography. We find that by whitening the bit stream with only one XOR operation, we pass all NIST tests. Our results demonstrate that medium energy barrier pMTJs are very promising candidates for true random number generation due to their easily controllable characteristics, while being robust towards environmental changes and material parameter variations. 
**References** 1Schuman, C. D. et al., arXiv:1705.06963.
2Vodenicarevic, D. et al., Physical Review Applied Vol. 8, 054045 (2017).
3Safranski, C. et al., Nano Letters Vol. 21, 2040–2045 (2021).
4Rehm, L. et al., Physical Review Applied Vol. 15, 034088 (2021).
 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8e61c8ec8ec8f3646e028cfc282d7a37.png)

Stochastic Magnetic Actuated Random Transducer Devices based on Perpendicular Magnetic Tunnel Junctions

Spin-Hall oscillators (SHOs) are promising spintronic devices to realize dc controlled GHz frequency signals in nanoscale devices for a variety of applications1,2, including for neuromorphic computing3. However, traditional SHOs have high auto-oscillation threshold currents and those based on magnetic tunnel junctions require a complex etching process. Here, we demonstrate that by combining a metallic ferromagnetic nanowire with low damping and high-quality ferromagnetic insulators, specifically epitaxial lithium aluminum ferrite thin films4, SHO characteristics are dramatically improved. Our magnetic bilayers SHOs are composed of Pt(5nm)/Py(5nm)/(Li0.5Al1.0Fe1.5O4 (LAFO) or Li0.5Al0.5Fe2O4 (LFO)) (x nm) layers with varied thicknesses x (including x=0, i.e. just Pt/Py layers) and two different compositions of insulator. The Pt/Py layers are patterned into 400 nm wide x 400 nm long nanowires between two Au contact pads as shown in Fig. 1a. Ferromagnetic resonance (FMR) measurements of the unpatterned heterostructure and spin-torque ferromagnetic resonance (ST-FMR) of micron-scale wires show that Py and LAFO are strongly ferromagnetically coupled and thus precess coherently. In the nanowires, we observe two prominent auto-oscillation modes in all samples, which we associate with bulk and edge spin-wave modes. Increased oscillator quality factor and maximum emission power (Fig. 1b) as well as lower threshold currents are obtained in samples containing LAFO and LFO. In addition, the maximum emission power and quality factor increases with the LAFO thickness. The performance can be further enhanced by replacing LAFO with LFO which possesses higher saturation magnetization. The improved characteristics are associated with the excitation of larger spin-precession angles and volumes in LAFO and LFO samples. We further find that the presence of LAFO enhances the auto-oscillation amplitude of spin-wave edge modes, consistent with our micromagnetic modeling. 
**References** 1 V.E. Demidov, S. Urazhdin, H. Ulrichs, V. Tiberkevich, A. Slavin, D. Baither, G. Schmitz, and S.O. Demokritov, Nat. Mater. 11, 1028 (2012).
2 Z. Duan, A. Smith, L. Yang, B. Youngblood, J. Lindner, V.E. Demidov, S.O. Demokritov, and I.N. Krivorotov, Nat. Commun. 5, 1 (2014).
3 J. Grollier, D. Querlioz, K. Y. Camsari, K. Everschor-Sitte, S. Fukami, and M. D. Stiles, Nature Electronics 3, 360 (2020)
4 X.Y. Zheng, L.J. Riddiford, J.J. Wisser, S. Emori, and Y. Suzuki, Appl. Phys. Lett. 117, 1 (2020).
 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/2ee2699e11bd6a21979c9c6278945c58.png)

Spin Hall oscillators based on ferromagnetic metal/lithium aluminum ferrite bilayers with enhanced output power and quality factor

Spin currents in magnetic random access memory (MRAM) devices being developed by the semiconductor industry are generated by passing an electrical current perpendicular to layers that form a magnetic tunnel junction [1]. However, it is now widely appreciated that current flow in the plane of a layer can generate significant spin currents through spin-orbit coupling, as first reported in heavy non-magnetic metal layers (e.g. Pt, Ta & W). In this case, however, the spin polarization is generally confined to the plane of the layers. An important research goal is to create a spin current with an arbitrary polarization, including one with a significant out-of-plane spin polarization to enable efficient switching and displacement of domain walls in perpendicularly magnetized layers. In this talk we discuss spin-orbit induced charge-to-spin conversion in various materials and nanostructures [2] and with magnetic materials. Specifically, we will report our observation of spin torques with a planar Hall effect symmetry from CoNi, with a spin polarization in the magnetization direction of the layer [3]. We found the strength of this effect to be comparable to that of the spin Hall effect in Pt, indicating that the planar Hall effect in ferromagnetic metals holds great promise as a spin current source with a controllable spin polarization direction.

**References:**

 [1] A. D. Kent and D. C. Worledge, Nature Nanotechnology 10, 187 (2015) [2] J-W. Xu and A. D. Kent, Physical Review Applied 14, 014012 (2020) [3] C. Safranski, J. Z. Sun, J-W., Xu and A. D. Kent, Physical Review Letters 124, 197204 (2020)

**Images:**

 Electrical Generation of Spin Currents

Perpendicular magnetic tunnel junctions, pMTJs, with a composite free layer have been developed and utilized in embedded memories and magnetic sensors. Such applications rely on fast current-induced switching of the free layer. Investigating the switching dynamics of the pMTJ free layer allows researchers to predict and optimize their switching speed. Experimental and micromagnetic simulation studies have been conducted toward this goal [1-3]. However, there continue to be challenges to overcome that are significant for technological applications. One major challenge in prediction and understating the spin transfer torque switching of the free layer is that its magnetic properties, such as magnetic anisotropy and magnetic exchange interaction, depends strongly on the details of the fabrication process and the materials involved. Recent studies suggest that the composite free layer, where a non-magnetic interlayer is inserted to enhance the perpendicular magnetic anisotropy and thermal stability of the free layer, the magnetic exchange constant is significantly lower than the bulk values [1]. The question is how does the reduced exchange interaction affect the spin torque switching dynamics and the switching speed of the free layer? Here we have investigated the effect of reduced exchange interaction on the spin torque switching dynamics and switching speed of the free layer of disk-shaped pMTJs. Our results show that when undergoing spin-transfer torque switching, the exchange interaction plays an important role in determining the switching path[4]: 1) the sequence of the micromagnetic events depends on the exchange interaction strength (see figure 1), and 2) the switching speed is greatly reduced when for lower exchange constants (see figure 2). Figure 1: A 30-nm pMTJ free layer undergoes a spin-torque switching when a long duration current pulse is applied to it (current is 1.6 times the critical current for switching). Material parameters are those mentioned in reference [1]. When exchange interaction is large (A=19 pJ/m), the switching is domain wall mediated [4]. For the same size element, when the exchange constant is smaller (A=8.5 pJ/m), the center of the element switches first, and this switched region moves to and hits the edge of the disk, and a domain wall is created across the element. By further reduced the exchange interaction (A=4 pJ/m), a droplet is formed at the center of the disk (fully reversed cells at the center), then this droplet hits the edge, and one or more domain walls form across the element. If the diameter of the disk is below a critical value [5], dc=16/π √(A/Keff ) where A is the exchange constant, and Keff is the uniaxial anisotropy that includes demagnetization energy and uniaxial perpendicular anisotropy, spin-torque switching of the free layer is expected to be a uniform macrospin model like switching. When the diameter of the disc is greater than dc, one or more domain walls (where the magnetization on one side of the wall is reversed and the other side is in the initial magnetic state) can form across the element, and dynamics are more complex. The structure of this domain wall and the magnetization profile of the free layer is very complex and gets even more complex for elements with smaller exchange interaction. In this presentation, I will present our results on how the reduced exchange interaction results in different (and more complex) dynamics that lead to a delayed switching [6]. I will also show that increasing the current does not necessarily make switching more coherent. ACKNOWLEDGEMENTS This research supported by Spin Memory Inc.

**References:**

 1. J. B. Mohammadi, B. Kardasz and A. D. Kent, ACS Applied Electronic Materials 1, 2025 (2019) 2. C. Hahn, G. Wolf and A. D. Kent, Phys. Rev. B94, 214432(2016) 3. Devolder, A. Le Goff and V. Nikitin, Phys. Rev. B93, 224432 (2016) 4. J. Beik Mohammadi and A. D. Kent, arXiv:2003.13875, 2020 (2020) 5. G. D. Chaves-O’Flynn, G. Wolf and A. D. Kent, Phys. Rev. Applied4, 024010 (2015) 6. N. Statuto, J. B. Mohammadi and A. D. Kent, Phys. Rev. B 103, 014409 (2021)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/f68c74c5ec5e7db532f030fdd1e876ea.jpg)
Figure 1: A 30-nm pMTJ free layer undergoes a spin-torque switching when a long duration current pulse is applied to it (current is 1.6 times the critical current for switching). Material parameters are those mentioned in reference [1]. When exchange interaction is large (A=19 pJ/m), the switching is domain wall mediated [4]. For the same size element, when the exchange constant is smaller (A=8.5 pJ/m), the center of the element switches first, and this switched region moves to and hits the edge of the disk, and a domain wall is created across the element. By further reduced the exchange interaction (A=4 pJ/m), a droplet is formed at the center of the disk (fully reversed cells at the center), then this droplet hits the edge, and one or more domain walls form across the element.

![](https://assets.underline.io/uploads/markdown_image/1/image/82849609136ca71b06e87913fb1a3f58.jpg)
Figure 2: Switching speed of a 30-nm pMTJ free layer vs. overdrive (that is applied voltage divided by the critical/minimum voltage required to switch the free layer). Different color symbols represent the simulated data for different exchange constant, and the solid lines are linear fit to each data set. As seen in this figure, the switching speed is greatly reduced as the exchange interaction is reduced. One interesting result is that although the switching sped vs. overdrive for each exchange constant value is fairly linear, as macrospin model suggests, the slope of the line is greatly reduced for elements with reduced exchange interaction (For example, compare the slope of the red line, that is for A=8.5 pJ/m, with the slope of the purple line, that represents the data with A=2 pJ/m).

 The Effect of Reduced Exchange Interactions on Switching of Perpendicular Magnetic Tunnel Junctions

DOC: Neuromorphic Computing

technical paper

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Stochastic Magnetic Actuated Random Transducer Devices based on Perpendicular Magnetic Tunnel Junctions

Spin Hall oscillators based on ferromagnetic metal/lithium aluminum ferrite bilayers with enhanced output power and quality factor

Electrical Generation of Spin Currents

The Effect of Reduced Exchange Interactions on Switching of Perpendicular Magnetic Tunnel Junctions

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